What is factor 32m^{15}-243n^{10} ?

The solution to factor 32m^{15}-243n^{10} is (2m^3-3n^2)(16m^{12}+24m^9n^2+36m^6n^4+54m^3n^6+81n^8)

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factor 32m^{15}-243n^{10}

factor

32 m^{15} - 243 n^{10}

(2 m^{3} - 3 n^{2}) (16 m^{12} + 24 m^{9} n^{2} + 36 m^{6} n^{4} + 54 m^{3} n^{6} + 81 n^{8})

Solution steps

32 m^{15} - 243 n^{10}

Rewrite

32 m^{15}

(2 m^{3})^{5}

Rewrite

243 n^{10}

(3 n^{2})^{5}

= (2 m^{3})^{5} - (3 n^{2})^{5}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

(2 m^{3})^{5} - (3 n^{2})^{5} = (2 m^{3} - 3 n^{2}) ((2 m^{3})^{4} + (2 m^{3})^{3} 3 n^{2} + (2 m^{3})^{2} (3 n^{2})^{2} + 2 m^{3} (3 n^{2})^{3} + (3 n^{2})^{4})

= (2 m^{3} - 3 n^{2}) ((2 m^{3})^{4} + (2 m^{3})^{3} 3 n^{2} + (2 m^{3})^{2} (3 n^{2})^{2} + 2 m^{3} (3 n^{2})^{3} + (3 n^{2})^{4})

Simplify

(2 m^{3} - 3 n^{2}) ((2 m^{3})^{4} + (2 m^{3})^{3} \cdot 3 n^{2} + (2 m^{3})^{2} (3 n^{2})^{2} + 2 m^{3} (3 n^{2})^{3} + (3 n^{2})^{4}) : (2 m^{3} - 3 n^{2}) (16 m^{12} + 24 m^{9} n^{2} + 36 m^{6} n^{4} + 54 m^{3} n^{6} + 81 n^{8})

= (2 m^{3} - 3 n^{2}) (16 m^{12} + 24 m^{9} n^{2} + 36 m^{6} n^{4} + 54 m^{3} n^{6} + 81 n^{8})

15 e^{2} + 28 e + 5

f (π) - g (π)

(3 x - 5) (3 x - 5)

4 0^{2} - 2 0^{2}

(X)^{2}

What is factor 32m^{15}-243n^{10} ?
The solution to factor 32m^{15}-243n^{10} is (2m^3-3n^2)(16m^{12}+24m^9n^2+36m^6n^4+54m^3n^6+81n^8)